1. Field of the Invention
The present invention is directed in general to magnetic resonance tomography (MRT) as employed in medicine for examining patients. The present invention is particularly directed to a method for the optimization of k-space trajectories in the location encoding of a magnetic resonance tomography apparatus. An optimally fast sampling of k-matrix achieved as a result thereof leads to the utmost effectiveness of the sequence employed.
2. Description of the Prior Art
MRT is based on the physical phenomenon of nuclear magnetic resonance and has been successfully employed in medicine and biophysics for more than 15 years. In this examination modality, the subject is subjected to a strong, constant magnetic field. As a result thereof, the nuclear spins in the subject align, these having been previously irregularly oriented. Radiofrequency energy can then excite these “ordered” spins to a specific oscillation. This oscillation generates the actual measured signal in MRT that is picked up with suitable reception coils. By utilizing non-uniform magnetic fields, which are generated by gradient coils, the test subject can be spatially encoded in all three spatial directions, which is generally referred to as “location encoding”.
The acquisition of the data in MRT ensues in k-space (frequency domain). The MRT image or spatial domain is obtained from the MRT data in k-space by means of Fourier transformation. The location encoding of the subject that k-space defines ensues by means of gradients in all three spatial directions. A distinction is made between the slice selection (defines an exposure slice in the subject, usually the Z-axis), the frequency encoding (defines a direction in the slice, usually the x-axis) and the phase encoding (defines the second dimension within the slice, usually the y-axis).
First, a slice is selectively excited, for example in the z-direction. The encoding of the location information in the slice ensues by means of a combined phase and frequency encoding with these two aforementioned, orthogonal gradient fields, which, for the example of a slice excited in z-direction, are generated by the gradient coils in the x-direction and the y-direction that have likewise already been mentioned.
FIGS. 6A and 6B show a first possible form of acquiring the data in an MRT scan. The sequence employed is a spin-echo sequence. With such a sequence, the magnetization of the spins is forced into the x-y-plane by means of a 90° excitation pulse. Over the course of time (½ TE; TE is the echo time), a dephasing of the magnetization component that together form the cross-magnetization in the x-y-plane Mxy occurs. After a certain time (for example, ½ TE), a 180° pulse is emitted in the x-y-plane so that the dephased magnetization components are mirrored without the precession direction and the precession times of the individual magnetization components being varied. After a further time duration ½ TE, the magnetization components again point in the same direction, i.e. a regeneration of the cross-magnetization that is referred to as “rephasing” occurs. The complete regeneration of the cross-magnetization is referred to as spin echo.
In order to measure an entire slice of the examination subject, the imaging sequence is repeated N-times for various values of the phase encoding gradient, for example Gy, with the frequency of the magnetic resonance signal (spin-echo signal) being sampled in every sequence repetition, and is digitalized and stored N-times in equidistant time steps Δt in the presence of the readout gradient Gx by means of the Δt-clocked ADC (analog-to-digital converter). According to FIG. 6B, a number matrix (matrix in k-space or k-matrix) with N×N data points is obtained in this way (a symmetrical matrix having N×N points is only an example; asymmetrical matrices also can be generated). An MR image of the observed slice having a resolution of N×N pixels can be directly reconstructed from this dataset by means of a Fourier transformation.
In a time-of-flight angiography with a magnetic resonance measurement, the imaging slice typically is oriented perpendicularly to the vessels to be presented. FIG. 4C schematically shows such an excitation slice 43. Contradictory demands are made on the repetition time TR in order to be able to produce an optimum contrast between the stationary tissue and the vessels 24.
The TR should be selected as short as possible in order to saturate the stationary tissue 23 as highly as possible. Given a flipping of the spins in immediate succession, there is not enough time for the magnetization to build up completely again in the longitudinal direction. This means that, given excitations in rapid succession, i.e. during a very short time TR, only s small magnetization vector Mz in terms of magnitude is regenerated in the longitudinal direction according to FIG. 4a, this also generating only a small signal after the flipping by the RF pulse. As a result, the stationary tissue 23 is shown very dark in the image. This is referred to as a saturation of the spins.
The spins of the blood 26 that flows through the vessels 23 to be presented are excited only when the blood 26 flows into the excitation layer 23. Since the blood has not yet experienced an RF excitation before entering into the excitation layer 23, the full (relaxed) magnetization of the spins of the blood M0 is available upon entry into the slice (see FIG. 4b). This results in the blood 26 flowing into the slice, and thus the blood-traversed vascular system, being shown brighter in the MRT image than the surrounding, stationary tissue 23. The ideal case would be an entry of the completely relaxed blood 26 into the slice 23 to be measured, a one-time excitation of the blood and, finally, an emergence of the once-stimulated blood from this slice before the next RF excitation ensues. This ideal case often cannot be achieved in reality since the slice thicknesses in the exposures of vascular anatomy are very large (approximately 4–6 cm), and the blood has a low flow velocity, especially in smaller vessels. Overall, the blood therefore experiences more than one excitation while flowing through the slice, leading to the blood at the “exit” end of the slice 25 exhibiting increasingly less contrast from the surrounding background tissue. In order to avoid this effect, the TR must be selected very high, i.e. sufficiently high so that the blood can flow through the entire slice block within the TR interval.
The spin saturation also can be influenced in the same way by the flip angle α. For example, a strong, fast saturation is achieved by means of a large flip angle. A small flip angle, however, leads to a fast relaxation of the flipped spins, so that the full longitudinal magnetization M0 is already available again after a very short time. Accordingly, the flip angle a should be large for a suppression of the stationary tissue but should be small for emphasizing the flowing blood.
In practice, the two demands—TR as short as possible for one reason but long for other reasons, and the flip angle a being very large for one reason but very small for other reasons—cannot be simultaneously satisfied, since they are contradictory. Conventionally, TR and/or a therefore are selected such that a compromise is found between the contradictory demands. The quality of the vessel presentation nonetheless continuously decreases with decreasing flow velocity of the blood.